Carbon-14 has a half-life of 5730 years. In a plant fossil, you find that the 14C has decayed to 1/4.00 of the original amount. How long ago was this plant alive?

We use the radioactive decay formula to solve this problem. It is expressed as:

An = Aoe^-kt

where An is the amount left in time t, Ao is the initial amount, k is the constant.

We first find the value of k from the half-life data. We do as follows:

An = Aoe^-kt

0.5 = e^-k (5730)

k = 1.21x10^-4

An = Aoe^-kt

1/4 = e^-1.21x10^-4t

t = 11456.98 years